Reinforced CMU Shear Wall In-Plane Shear (TMS 402 ASD)
The allowable in-plane shear of a reinforced, fully grouted masonry shear wall: the masonry term Fvm = 0.5 x ((4.0 - 1.75 M/(V dv)) sqrt(f'm)) + 0.25 P/An that grows with axial compression and shrinks with slenderness, the horizontal-steel term Fvs = 0.5 Av Fs dv/(An s), and the combined stress against the shear-span-graded 3-to-2 sqrt(f'm) cap, times the net area for the allowable force. An 8 in by 8 ft wall under 20 kip of axial with #4 horizontals at 48 in carries 76 psi and 55.7 kip -- the capacity the seismic-base-shear demand is checked against. Sustained axial only; special-reinforced detailing is separate. A design aid, not a substitute for the engineer of record's stamped lateral design.
Formula and source
Fvm = 0.5 x ((4.0 - 1.75 x M/(V dv)) x sqrt(f'm)) + 0.25 x (P/An); Fvs = 0.5 x (Av Fs dv)/(An s); Fv = Fvm + Fvs, capped at 3 sqrt(f'm) (M/(V dv) <= 0.25) grading to 2 sqrt(f'm) (>= 1.0); Va = Fv An.
TMS 402-16 (ACI 530 / ASCE 5) allowable-stress in-plane shear provisions, as compiled in the Masonry Designers' Guide and CMHA TEK 14-07C, by name.
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